Won't work. This is a (now) classical trick integration problem; there is no closed-form antiderivative. You have to exploit some kind of symmetry in the integral. The substitution u = 3 - x makes the integral a little prettier. Then one more substitution will change the integrand but not the integral signs; maybe you can add, subtract, or multiply the original integral with the transformed one and get something nicer. Often times these things end up being recursive, i.e., you get that the value of the integral is (something) plus the value of the integral, so the integral is that (something) divided by two.
There are lots of tricks you can use, but only a few very specific ones will give you the right answer, and you probably didn't do much of these types of problems in calc 1/2.
Luke Bailey
Yeah ok. A couple times I accidentally copied a question wrong and ended up with some recursive shit that drove me nuts.
Christian Myers
the problem with mathematics is that you can study it for years until you finally reach the point of using it, and it can take 10,20 or even 30 years until you apply mathematics to something. this is why kids hate math, its because they can't see the light in the end of the tunnel. most of the stuff they will forget eventually, and they will have to constantly refresh. if we had a way to show students how math is applied in various fields, people would be much more inclined to study it. but there is a barrier of autism between academy and industry that people don't talk about. so practicing math has become a "sport" of people trying to get the right answer for nothing. this applies to everything in life, you can study music theory for years but you never seen a fucking guitar then you won't know how to play it. even if you have the same theory in mind like Beethoven did
Easton Perez
Recursive integrals are great though. If you see what you started with in your solution, you're almost done!
Liam Jackson
how? You have to integrate again forever
Samuel Bailey
Here's an example.
Adrian Hall
but it's not done
Wyatt Collins
But it is done. I left out the integral of sec(x) because it's not really important, but just replace it with ln|sec(x) + tan(x)| + C if you want.
Landon Myers
now I feel stupid but what if you got something that wasn't really done, just do that again?
Easton Williams
If you're trying to find out what I is, and you get an expression that includes I, just solve it like you would any equation:
x = 15 - x
2x = 15
x = 15/2
I'm not sure what you mean by "wasn't really done," this is just one example of a case where integrating by parts gives you an expression in terms of the original integral so we can use this trick.
